We consider the 3-user bidirectional communication system in Fig\(.\)  REF  comprising of a FD MIMO node \(k\)  equipped with \(N_k\)  TX and \(M_k\)  RX antenna elements, and two HD multi-antenna nodes \(q\)  and \(m\)  having \(M_q\)  and \(N_m\)  antennas, respectively. It is assumed that node \(k\)  communicates simultaneously (in the same time and frequency resources) with node \(q\)  in the DL and node \(m\)  in the UL. All nodes are considered capable of performing digital beamforming, which for simplicity we assume to be realized with linear filters. Node \(k\)  is also capable of analog TX/RX beamforming using the partially connected HBF architecture [1]}, as will be detailed in the sequel.
